Mesoscopic Nonequilibrium Thermodynamics Gives the Same Thermodynamic Basis to Butler−Volmer and Nernst Equations

Mesoscopic nonequilibrium thermodynamics is used to derive the Butler−Volmer equation, or the stationary state nonlinear relation between the electric current density and the overpotential of an electrode surface. The equation is derived from a linear flux−force relationship at the mesoscopic level for the oxidation of a reactant to its charged components. The surface was defined with excess variables (a Gibbs surface). The Butler−Volmer equation was derived using the assumption of local electrochemical equilibrium in the surface on the mesoscopic level. The result was valid for an isothermal electrode with reaction-controlled charge transfer and with equilibrium for the reactant between the adjacent bulk phase and the surface. The formulation that is used for the mesoscopic level is consistent with nonequilibrium thermodynamics for surfaces and, thus, with the second law of thermodynamics. The Nernst equation is recovered in the reversible limit. The reversible/dissipative nature of the charge-transfer process is discussed on this basis.